arXiv 13 Sep 2026 · Econometrics
arXiv:2609.14398 · PDF · Extracted main text
Two frequent approaches for identifying structural VARs are external instruments, which carry economic content but are often weak, and non-Gaussianity of the shocks which provides statistical identification but carries no economic meaning. We combine the two strategies in a single generalized method of moments framework that stacks proxy exclusion restrictions with higher-order moment conditions of the structural shocks. This hybrid approach point-identifies the target shocks while also identifying the non-target shocks up to sign and ordering. Under suitable rank conditions, the higher-order moments anchor the identification uniformly over the instrument strength. Consequently, under local-to-zero proxy relevance, estimators of the dynamic causal effects remain consistent, and standard asymptotic inference remains valid. Moreover, the Anderson-Rubin confidence sets are substantially narrower than their instrument-only counterparts. The hybrid estimator is also more efficient than either source of identification used in isolation: at any fixed proxy relevance, even a weak instrument increases efficiency of the estimator through its covariance with the non-Gaussian moment block. Under local deviations from proxy exogeneity, we provide asymptotic bias bounds and show that stronger non-Gaussianity of the shocks compresses the bias. Finally, the over-identified structure yields two mutually orthogonal specification tests, for proxy exogeneity and validity of higher-order moment conditions. We derive their limiting distributions and provide a bootstrap procedure for finite-sample critical values. Monte Carlo simulations and two applications with identification of oil news-shock and a Euro-area MP shock demonstrate the potential of our framework.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Newey, Whitney K (1985) Generalized method of moments specification testing | 0.928 | 4 | 4 | 100% |
| 2 | Montiel Olea, José L. and Stock, James H. and Watson, Mark W (2021) Inference in Structural Vector Autoregressions identified with an external instrument | 0.855 | 8 | 5 | 62% |
| 3 | Känzig, Diego R (2021) The Macroeconomic Effects of Oil Supply News: Evidence from OPEC Announcements | 0.855 | 8 | 4 | 62% |
| 4 | Brüggemann, Ralf and Jentsch, Carsten and Trenkler, Carsten (2016) Inference in VARs with conditional heteroskedasticity of unknown form | 0.843 | 4 | 4 | 75% |
| 5 | Jentsch, Carsten and Lunsford, Kurt G (2022) Asymptotically Valid Bootstrap Inference for Proxy SVARs | 0.843 | 4 | 4 | 75% |
| 6 | Comon, Pierre (1994) Independent component analysis, A new concept? | 0.843 | 5 | 4 | 60% |
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| 8 | Kilian, Lutz (2024) How to construct monthly VAR proxies based on daily surprises in futures markets | 0.811 | 4 | 2 | 100% |
| 9 | Lanne, Markku and Luoto, Jani (2021) GMM Estimation of Non-Gaussian Structural Vector Autoregression | 0.811 | 4 | 2 | 100% |
| 10 | Gertler, Mark and Karadi, Peter (2015) Monetary Policy Surprises, Credit Costs, and Economic Activity | 0.737 | 5 | 3 | 40% |
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